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(15 pts) A fair coin is tossed four times and the events A, B, and C are defined as follows: A (At least one head is observed B: At least two heads are observed C (The number of heads observed is odd Find the following probabilities: (a) P(BC) (b) P(BCnc)-

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Answer #1

a)P(Bc)=P(at most 1 head)=P(X=0)+P(X=1)=4C0(1/2)0(1/2)4+4C1(1/2)1(1/2)3=0.0625+0.25=0.3125

b)P(Bc n C) =P(X=1)=4C1(1/2)1(1/2)3=0.25

c) P(Ac u Bc u C)=P(X=0)+P(X=1)+P(X=3)= 4C0(1/2)0(1/2)4+4C1(1/2)1(1/2)3+4C3(1/2)3(1/2)1

=0.0625+0.25+0.25=0.5625

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